Biquadratic fields having a non-principal Euclidean ideal class
| Autor: | Jaitra Chattopadhyay, S. Muthukrishnan |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Class (set theory)
Algebra and Number Theory Ideal (set theory) Mathematics - Number Theory Degree (graph theory) Generalization 010102 general mathematics Principal (computer security) 11A05 010103 numerical & computational mathematics Algebraic number field 01 natural sciences Combinatorics Euclidean geometry FOS: Mathematics Number Theory (math.NT) 0101 mathematics Mathematics |
| Zdroj: | Journal of Number Theory. 204:99-112 |
| ISSN: | 0022-314X |
| DOI: | 10.1016/j.jnt.2019.03.015 |
| Popis: | H. W. Lenstra \cite{lenstra} introduced the notion of an Euclidean ideal class, which is a generalization of norm-Euclidean ideals in number fields. Later, families of number fields of small degree were obtained with an Euclidean ideal class (for instance, in \cite{hester1} and \cite{cathy}). In this paper, we construct certain new families of biquadratic number fields having a non-principal Euclidean ideal class and this extends the previously known families given by H. Graves \cite{hester1} and C. Hsu \cite{cathy}. Comment: It is a preliminary version. Comments and suggestions are welcome |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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